Geodesic
Minimal branches of solutions of nonlinear operator equations in Banach spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 183 (2020), pp. 113-119

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the nonlinear equation $B(\lambda)x=R(x,\lambda)+b(\lambda)$, where $R(0,0)=0$, $b(0)=0$, the linear operator $B(\lambda)$ has a bounded inverse operator for $S\ni\lambda\rightarrow0$, and $S$ is an open set, $0\in\partial S$. We examine the problem on the existence of a small continuous solution of the maximal order od smallness $x(\lambda)\rightarrow0$ as $S\ni\lambda\rightarrow0$. A constructive method way of constructing this solution is presented.
Keywords: nonlinear operator, Banach space, operator equation, minimal branch. 
@article{INTO_2020_183_a9,
     author = {R. Yu. Leontiev},
     title = {Minimal branches of solutions of nonlinear operator equations in {Banach} spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {113--119},
     publisher = {mathdoc},
     volume = {183},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_183_a9/}
}
TY  - JOUR
AU  - R. Yu. Leontiev
TI  - Minimal branches of solutions of nonlinear operator equations in Banach spaces
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 113
EP  - 119
VL  - 183
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_183_a9/
LA  - ru
ID  - INTO_2020_183_a9
ER  - 
%0 Journal Article
%A R. Yu. Leontiev
%T Minimal branches of solutions of nonlinear operator equations in Banach spaces
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 113-119
%V 183
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_183_a9/
%G ru
%F INTO_2020_183_a9
R. Yu. Leontiev. Minimal branches of solutions of nonlinear operator equations in Banach spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 183 (2020), pp. 113-119. http://geodesic.mathdoc.fr/item/INTO_2020_183_a9/